Electronic Structure of Materials

Adrian P. Sutton

Electronic Structure of Materials

Adrian P. Sutton

Description

In recent years, researchers have increasingly recognized the dominant role of the local atomic environment in controlling the electronic structure and properties of materials. This recognition has spawned the "real-space" approach that provides a coherent framework for the study of perfect and defective crystals and non-crystalline materials. In addition to presenting these ideas, this text details the reciprocal-space approach--exemplified in band theory--and draws powerful links between the two approaches. The book includes illustrations and examples of many up-to-date calculations based on density functional theory that are used today as predictive tools in materials science. Throughout the book, the mathematical complexity is kept to a minimum, while comprehensive problem sets allow readers to master the fundamental concepts. The text provides for students in materials science, physics, and chemistry a unique introduction to predictive modelling of the electronic structure and properties in today's materials.

Electronic Structure of Materials

Adrian P. Sutton

Table of Contents

1. Introduction1.1. Aims of the Book1.2. The "Universal" Equation of State for Metals1.3. Structure Maps1.4. The Hydrogen Atom1.5. Metals, Semiconductors, and Insulators2. The Diatomic Molecule2.1. The Review of Bras, Kets and All That2.2. A Homonuclear Diatomic Molecule: The Hydrogen Molecule2.3. A Heteronuclear Diatomic Molecule2.4. Electronegativity2.5. Bond Energy and Bond Order3. From the Finite to the Infinite3.1. Chain Molecules and K-Space3.2. Bond Order in an Infinite System3.3. The Density of States: Total and Local3.4. Band Energy and Bond Energy3.5. The Moments Theorem4. Into Two and Three Dimensions4.1. Solids as Giant Molecules4.2. The Square Lattice4.3. The Simple Cubic Lattice4.4. Brillouin Zones for the B.C.C. and F.C.C. Lattices4.5. Equation of Motion of an Electron under an External Force4.6. Holes4.7. The Fermi Surface4.8. The Density of States in Two-dimensional and Three-dimensional crystals4.9. The Density Matrix, Bond Order, and Bond Energy4.10. The Moments Theorem Applied to Two-dimensional and Three-dimensional Crystals5. Band Gaps: Origins and Consequences5.1. Band Gaps5.2. Infinite Linear Chain with Two S-States per Atom5.3. Energy Gap in a Binary AB Alloy Linear Chain Crystal5.4. Peierls Distortions5.5. Metals, Insulators, and the Metallic Bond6. S-P Bonding--A Case Study in Silicon6.1. S-P Bonding6.2. S-P bonding between Two Silicon Atoms6.3. Angular Dependence of S-P and P-P Hopping Integrals6.4. SP Hybrids6.5. Simple Models of the Electronic Structure of Tetrahedrally Bonded Silicon6.6. The Band Structure of Silicon in a Minimal Atomic Basis Set6.7. The Bond Order and Bond Energy in Silicon in a Minimal Atomic Basis Set7. Free Electron Theory7.1. Introduction to Free Electron Theory7.2. The Free Electron Approximation7.3. Electronics in a Box7.4. Density of States7.5. Free Electron Bands and LCAO Bands7.6. The Nearly Free Electron Model8. Properties of Free Electron Metals8.1. Fermi-Dirac Statistics8.2. Contact Potential8.3. Electronic Specific Heat8.4. Electrical Conductivity of Metals8.5. Thermal Conductivity of Metals8.6. The Wiedemann-Franz Ratio8.7. The Hall Effect8.8. The Cohesive Energy of Simple Metals and Its Volume Dependence8.9. Structural Energy Differences9. The Transition Metals9.1. The Transition Metals9.2. The Friedel Model9.3. The Friedel Model in the Second Moment Approximation9.4. Finnis-Sinclair Potentials for Computer Simulations of Transition Metals9.5. D-D Bonding9.6. Changes in Crystal Structure Across the Transition Metal Series9.7. Bonding in Metallic Alloys10. Structural Stability of Compounds10.1. Hybridization and Crystal Structural Stability10.2. Atomic Factors Influencing the Structures of Compounds10.3. Structure Maps10.4. Applications of Structure Maps11. Introduction to Modern Quantitative Theory11.1. Modern Quantitative Predictions of Crystal Structure and Stability11.2. The Born-Oppenheimer Approximation11.3. Outline of Density Functional Theory11.4. Applications12. Where Band Theory Breaks Down12.1. Electrons in Non-crystalline Materials12.2. The Energy Gap in Amorphous Silicon12.3. Electron Localization12.4. Polarons12.5. Anderson Localization12.6. Metal-Insulator Transitions, Or What is a Metal?Set Problems